Problem: Each month the balance, $B$, of Harper's loan increases by $0.22\%$ and decreases by $\$250.00$. Which equation describes this relationship? Choose 1 answer: Choose 1 answer: (Choice A) A $B(t)=0.0022B-250$ (Choice B) B $\dfrac{dB}{dt}=0.0022B-250$ (Choice C) C $B(t)=0.0022(B-250)$ (Choice D) D $\dfrac{dB}{dt}=0.0022(B-250)$
Solution: The balance of the loan is denoted by $B$. The rate of change of the balance is represented by $B'(t)$, or $\dfrac{dB}{dt}$. The balance increases by $0.22\%$, so we can represent that change as $0.0022B$. Then it decreases by $250$. In conclusion, the equation that describes this relationship is $\dfrac{dB}{dt}=0.0022B-250$.